Skeletal Muscle Fascicle Arrangements Can Be Reconstructed Using a Laplacian Vector Field Simulation

Abstract

Skeletal muscles are characterized by a large diversity in anatomical architecture and function. Muscle force and contraction are generated by contractile fiber cells grouped in fascicle bundles, which transmit the mechanical action between origin and insertion attachments of the muscle. Therefore, an adequate representation of fascicle arrangements in computational models of skeletal muscles is important, especially when investigating three-dimensional muscle deformations in finite element models. However, obtaining high resolution in vivo measurements of fascicle arrangements in skeletal muscles is currently still challenging. This motivated the development of methods in previous studies to generate numerical representations of fascicle trajectories using interpolation templates. Here, we present an alternative approach based on the hypothesis of a rotation and divergence free (Laplacian) vector field behavior which reflects observed physical characteristics of fascicle trajectories. To obtain this representation, the Laplace equation was solved in anatomical reconstructions of skeletal muscle shapes based on medical images using a uniform flux boundary condition on the attachment areas. Fascicle tracts were generated through a robust flux based tracing algorithm. The concept of this approach was demonstrated in two-dimensional synthetic examples of typical skeletal muscle architectures. A detailed evaluation was performed in an example of the anatomical human tibialis anterior muscle which showed an overall agreement with measurements from the literature. The utility and capability of the proposed method was further demonstrated in other anatomical examples of human skeletal muscles with a wide range of muscle shapes and attachment morphologies.

A computational approach to calculate personalized pennation angle based on MRI: effect on motion analysis

“…Representations of the muscle fiber orientations in the subject-specific anatomical models were generated using the Laplacian-based method [10,11]. The theoretical foundation of Laplace-based method relies on the conceived physical properties of the muscle fiber bundles, which are parallelly aligned and run continuously between attachment areas to transmit the muscle forces between skeletal elements.…”

“…A zero gradient is applied on the bulk surface of the muscle to avoid termination of the fiber bundles outside the attachment areas. A uniform flux can be applied at the attachment surfaces such that the mass equation is respected, which allows for the generation of physically plausible muscle fiber directions as previously demonstrated [10]. The general workflow of the Laplacian approach is summarized in Fig.…”

“…The changes in moments, tendon forces, and muscle forces were extracted from OpenSim and are related to each other according to Eqs. [8][9][10][11].…”

Subject-specific assessment of loading variation in the knee ligaments with a view to preoperative planning

“…The ligaments fibers were generated with a method which allows to construct a numerical representation of the fiber orientations as a Laplacian vector field [13].…”

Reconstruction of muscle fascicle architecture from iodine-enhanced microCT images: A combined texture mapping and streamline approach

“…Moreover, many physiological principles of skeletal muscle mechanics can only be investigated using a more detailed and realistic representation of the fibre bundles within the muscle model as it is the case with chemo-electromechanical (CEM) models as proposed by Röhrle (2010) and Röhrle (2013, 2014). For their use within volumetric muscle models, fascicle distributions can be approximated, for example, by fitting fascicle templates to muscle outer geometries obtained from MRI data (Blemker and Delp, 2005), or by combining the digitised information of the muscle insertion and origin with techniques known from elliptic grid generation (Choi and Blemker, 2013;Knupp and Steinberg, 1993). Furthermore, based on a detailed data set of digitised fibres from a cadaver, Sánchez et al (2014) have developed a workflow to embed the digitised fibres within subject-specific muscle geometries.…”